Solve for $x$ and $y$ using elimination. ${-x+2y = 8}$ ${-4x+5y = 14}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-4$ ${4x-8y = -32}$ $-4x+5y = 14$ Add the top and bottom equations together. $-3y = -18$ $\dfrac{-3y}{{-3}} = \dfrac{-18}{{-3}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {-x+2y = 8}\thinspace$ to find $x$ ${-x + 2}{(6)}{= 8}$ $-x+12 = 8$ $-x+12{-12} = 8{-12}$ $-x = -4$ $\dfrac{-x}{{-1}} = \dfrac{-4}{{-1}}$ ${x = 4}$ You can also plug ${y = 6}$ into $\thinspace {-4x+5y = 14}\thinspace$ and get the same answer for $x$ : ${-4x + 5}{(6)}{= 14}$ ${x = 4}$